TSTP Solution File: ALG363-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG363-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:43:04 EDT 2023
% Result : Unsatisfiable 38.45s 5.35s
% Output : Proof 38.45s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG363-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 03:49:29 EDT 2023
% 0.14/0.34 % CPUTime :
% 38.45/5.35 Command-line arguments: --no-flatten-goal
% 38.45/5.35
% 38.45/5.35 % SZS status Unsatisfiable
% 38.45/5.35
% 38.45/5.35 % SZS output start Proof
% 38.45/5.35 Take the following subset of the input axioms:
% 38.45/5.36 fof(cls_add__nonneg__pos_0, axiom, ![T_a, V_a, V_b]: (~class_OrderedGroup_Opordered__comm__monoid__add(T_a) | (c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), T_a) | (~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a), V_b, T_a) | ~c_lessequals(c_HOL_Ozero__class_Ozero(T_a), V_a, T_a))))).
% 38.45/5.36 fof(cls_conjecture_0, negated_conjecture, ~c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(v_f____(v_x))), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 38.45/5.36 fof(cls_exp__eq__one__iff_1, axiom, c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)=c_HOL_Oone__class_Oone(tc_RealDef_Oreal)).
% 38.45/5.36 fof(cls_exp__gt__zero_0, axiom, ![V_x]: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oexp(V_x, tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 38.45/5.36 fof(cls_rp_0, axiom, c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_r, tc_RealDef_Oreal)).
% 38.45/5.36 fof(cls_th_0, axiom, ![V_n]: c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(V_n)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 38.45/5.36 fof(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add, axiom, class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal)).
% 38.45/5.36
% 38.45/5.36 Now clausify the problem and encode Horn clauses using encoding 3 of
% 38.45/5.36 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 38.45/5.36 We repeatedly replace C & s=t => u=v by the two clauses:
% 38.45/5.36 fresh(y, y, x1...xn) = u
% 38.45/5.36 C => fresh(s, t, x1...xn) = v
% 38.45/5.36 where fresh is a fresh function symbol and x1..xn are the free
% 38.45/5.36 variables of u and v.
% 38.45/5.36 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 38.45/5.36 input problem has no model of domain size 1).
% 38.45/5.36
% 38.45/5.36 The encoding turns the above axioms into the following unit equations and goals:
% 38.45/5.36
% 38.45/5.36 Axiom 1 (clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add): class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) = true2.
% 38.45/5.36 Axiom 2 (cls_exp__eq__one__iff_1): c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal).
% 38.45/5.36 Axiom 3 (cls_rp_0): c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_r, tc_RealDef_Oreal) = true2.
% 38.45/5.36 Axiom 4 (cls_add__nonneg__pos_0): fresh613(X, X, Y, Z, W) = true2.
% 38.45/5.36 Axiom 5 (cls_exp__gt__zero_0): c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oexp(X, tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 38.45/5.36 Axiom 6 (cls_add__nonneg__pos_0): fresh475(X, X, Y, Z, W) = c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(Y), c_HOL_Oplus__class_Oplus(Z, W, Y), Y).
% 38.45/5.36 Axiom 7 (cls_add__nonneg__pos_0): fresh612(X, X, Y, Z, W) = fresh613(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(Y), W, Y), true2, Y, Z, W).
% 38.45/5.36 Axiom 8 (cls_add__nonneg__pos_0): fresh612(class_OrderedGroup_Opordered__comm__monoid__add(X), true2, X, Y, Z) = fresh475(c_lessequals(c_HOL_Ozero__class_Ozero(X), Y, X), true2, X, Y, Z).
% 38.45/5.36 Axiom 9 (cls_th_0): c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(X)), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 38.45/5.36
% 38.45/5.36 Goal 1 (cls_conjecture_0): tuple2(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(v_f____(v_x))), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)) = tuple2(true2, true2).
% 38.45/5.36 Proof:
% 38.45/5.36 tuple2(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(v_f____(v_x))), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 38.45/5.36 = { by axiom 9 (cls_th_0) }
% 38.45/5.36 tuple2(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), true2)
% 38.45/5.36 = { by axiom 6 (cls_add__nonneg__pos_0) R->L }
% 38.45/5.36 tuple2(fresh475(true2, true2, tc_RealDef_Oreal, v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), true2)
% 38.45/5.36 = { by axiom 3 (cls_rp_0) R->L }
% 38.45/5.36 tuple2(fresh475(c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_r, tc_RealDef_Oreal), true2, tc_RealDef_Oreal, v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), true2)
% 38.45/5.36 = { by axiom 8 (cls_add__nonneg__pos_0) R->L }
% 38.45/5.36 tuple2(fresh612(class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), true2)
% 38.45/5.36 = { by axiom 1 (clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) }
% 38.45/5.36 tuple2(fresh612(true2, true2, tc_RealDef_Oreal, v_r, c_HOL_Oone__class_Oone(tc_RealDef_Oreal)), true2)
% 38.45/5.36 = { by axiom 2 (cls_exp__eq__one__iff_1) R->L }
% 38.45/5.36 tuple2(fresh612(true2, true2, tc_RealDef_Oreal, v_r, c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)), true2)
% 38.45/5.36 = { by axiom 7 (cls_add__nonneg__pos_0) }
% 38.45/5.36 tuple2(fresh613(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), true2, tc_RealDef_Oreal, v_r, c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)), true2)
% 38.45/5.36 = { by axiom 5 (cls_exp__gt__zero_0) }
% 38.45/5.36 tuple2(fresh613(true2, true2, tc_RealDef_Oreal, v_r, c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)), true2)
% 38.45/5.36 = { by axiom 4 (cls_add__nonneg__pos_0) }
% 38.45/5.36 tuple2(true2, true2)
% 38.45/5.36 % SZS output end Proof
% 38.45/5.36
% 38.45/5.36 RESULT: Unsatisfiable (the axioms are contradictory).
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